The Feynman-Kac Formula, named for Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes, expressing the solution of certain such equations as an expected value taken over the paths of an associated random process. The formula arose in 1947 after Kac, hearing Feynman present his path-integral approach to quantum mechanics at Cornell University, realized the two of them were working on the same underlying idea from different directions, and it provides a rigorous real-valued counterpart to Feynman's heuristic path integrals. The corresponding complex-valued case needed directly in quantum mechanics remains, by the source's own account, an open question.
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Source Feynman-Kac formula, Wikipedia
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When originally published by Kac in 1949, the formula was presented as a means for determining the distribution of certain Wiener functionals.
Proved By: Mark Kac, Lead sentence
The Feynman-Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes.
In Branch: Differential Equations, Lead sentence
Kac, establishes a link between parabolic partial differential equations and stochastic processes.
In Group: Stochastic Processes and Martingales, Lead section
link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty
View the SourceMark Kac (MacTutor)
Principal Result Of: Mark Kac, Biography, Feynman-Kac path integralQuote, Principal Result Of: Mark Kac, Biography, Feynman-Kac path integral
The method of quantization now in use involves the Feynman -Kac path integral, named after Richard Feynman and Mark Kac.
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